Answer: 20.73 m/s
Explanation:
The centripetal force is given by the following equation:
[tex]F_{c}=m a_{c}[/tex] (1)
Where:
[tex]F_{c}=2600 N[/tex] is the centripetal force
[tex]m=1200 kg[/tex] is the mass of the car
[tex]a_{c}[/tex] is the centripetal acceleration
Isolating [tex]a_{c}[/tex]:
[tex]a_{c}=\frac{F_{c}}{m}[/tex] (2)
[tex]a_{c}=\frac{2600 N}{1200 kg}[/tex] (3)
[tex]a_{c}=2.16 m/s^{2}[/tex] (4)
Now, there is a relation between the centripetal acceleration and the tangential velocity:
[tex]a_{c}=\frac{V^{2}}{r}[/tex] (5)
Where [tex]V[/tex] is the tangential velocity and [tex]r[/tex] is the radius of the circular path, which can be found if we know its length [tex]l=1.25 km=1250 m[/tex]:
[tex]l=2 \pi r[/tex] (6)
[tex]r=\frac{l}{2 \pi}[/tex] (7)
[tex]r=\frac{1250 m}{2 \pi}[/tex] (8)
[tex]r=198.94 m[/tex] (9)
Substituting (4) and (8) in (5)
[tex]2.16 m/s^{2}=\frac{V^{2}}{198.94 m}[/tex] (5)
Finding [tex]V[/tex]:
[tex]V=20.729 m/s \approx 20.73 m/s[/tex]
